Subgroups — C₇×Q₈⋊C₂₇ #13094125

Order 1512.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
2	C₂×C₇×C₂₇	—	4	1	no	maximal
3	C₄×C₇×C₉	—	3	1	no	—
4	Q₈⋊C₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₂₇	—	4	1	no	Hall
6	C₃×C₇×Q₈	C₉	1	1	yes	characteristic
7	C₂×C₇×C₉	A₄	1	1	yes	characteristic
8	C₃×C₄×C₇	—	3	1	no	—
9	Q₈×C₉	C₃×C₇	1	1	yes	characteristic
10	C₇×C₉	SL(2,𝔽₃)	1	1	yes	characteristic
11	C₇×Q₈	C₂₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₂₇	—	4	1	no	—
13	C₂×C₃×C₇	C₂²⋊C₉	1	1	yes	characteristic
14	C₄×C₉	—	3	1	no	—
15	C₄×C₇	—	3	1	no	—
16	C₂₇	—	4	1	no	Sylow
17	C₃×Q₈	C₇×C₉	1	1	yes	characteristic
18	C₃×C₇	Q₈⋊C₉	1	1	yes	characteristic
19	C₂×C₉	C₇×A₄	1	1	yes	characteristic
20	C₂×C₇	C₂²⋊C₂₇	1	1	yes	characteristic
21	C₃×C₄	—	3	1	no	—
22	C₉	C₇×SL(2,𝔽₃)	1	1	yes	characteristic
23	Q₈	C₇×C₂₇	1	1	yes	characteristic, complemented, Sylow
24	C₇	Q₈⋊C₂₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	C₇×C₂²⋊C₉	1	1	yes	characteristic
26	C₄	—	3	1	no	—
27	C₃	C₇×Q₈⋊C₉	1	1	yes	characteristic
28	C₂	C₇×C₂²⋊C₂₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.